Balancing of mixed-model parallel U-shaped assembly lines considering model sequences

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(1)ORE Open Research Exeter. TITLE Balancing of mixed-model parallel U-shaped assembly lines considering model sequences AUTHORS Kucukkoc, I; Zhang, DZ JOURNAL International Journal of Production Research DEPOSITED IN ORE 18 May 2017. This version available at http://hdl.handle.net/10871/27576. COPYRIGHT AND REUSE Open Research Exeter makes this work available in accordance with publisher policies.. A NOTE ON VERSIONS The version presented here may diﬀer from the published version. If citing, you are advised to consult the published version for pagination, volume/issue and date of publication.

(2) International Journal of Production Research. ie. ev. rR. ee. rP Fo w. Balancing of mixed-model parallel U-shaped assembly lines considering model sequences. Manuscript ID. Date Submitted by the Author: Complete List of Authors:. Keywords: Keywords (user):. International Journal of Production Research TPRS-2015-IJPR-1915.R2 Special Issue Paper 25-Aug-2016. ly. Manuscript Type:. On. Journal:. Kucukkoc, Ibrahim; University of Exeter, College of Engineering, Mathematics and Physical Sciences; Balikesir University, Industrial Engineering Department Zhang, David; University of Exeter, College of Engineering, Mathematics and Physical Sciences; Chongqing University, State Key Laboratory on Mechanical Transmission ASSEMBLY LINE BALANCING, DESIGN OF PRODUCTION SYSTEMS, PRODUCTION PLANNING U-shaped assembly lines, mixed-model assembly lines. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(3) Page 1 of 37. w. ie. ev. rR. ee. rP Fo ly. On. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(4) International Journal of Production Research. Detailed Response to Reviewers Dear Reviewers, Thanks for reviewing the paper and providing your useful comments once again. All comments have been handled individually. Please find below the detailed responses to your comments.. Reviewer #1: Comment 1-1: My decision is accepting. Response 1-1: Thank you for your comment. We are happy to see that you found the changes made in the manuscript in the previous round satisfactory.. rP Fo. Reviewer #2. Comment 2-1: In response 2‐1 provided by the authors, they state that " this paper gives an insight about the mixed‐model U‐line idea which has potential application opportunities to produce large‐sized products such as buses, trucks and cars." This response shows that the concept is so far from practice and industrial realities. Because, as originated from Toyota, U‐shaped assembly lines are designed for small products or parts and these lines have small number of tasks. Therefore, the paper is not suitable for publication in IJPR. Response 2-1: Thank you for your comment. The following image (see Fig. 1) shows the practical application of a hybrid U-shaped line at a Japanese leading car manufacturer’s assembly plant1.. w. ie. ev. rR. ee. ly. On. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 2 of 37. Fig. 1. U-line configuration at Honda’s car assembly plant1. If the U-shaped line is aimed to be utilised for producing small products (as you said), then it can have a layout which limits working in between the two branches of the line. In other words, no space is available between the two (front and back) branches of the line to locate operators/workstations. Instead, the workstations can be located to the outer side of the line which limits access to the inner side. It is clear that such a configuration is not practical for producing large items, e.g. cars. However, the Uline configuration given in Fig. 1 allows performing tasks on both sides of the product being assembled on the line. Therefore, there is no doubt that such a configuration can easily be applied for producing large-sized products. 1. http://s3.caradvice.com.au/thumb/480/240/wp-content/uploads/2016/04/honda-cell-production-plant-ARCfactory-01.jpg. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(5) Page 3 of 37. Reviewer #3 Comment 3-1: The paper can be accepted in its current form. Response 3-1: Thank you for your comment and encouraging thoughts in the previous round.. Reviewer #4 Comment 4-Overall: The paper deals with the balancing problem of mixed model U‐lines in a parallel U‐shaped line system as the authors called. It seems that the paper is a modified version of their previous study which deals with the problem of balancing parallel single model U‐lines (Kucukkoc and Zhang, 2015a) by considering the lines are mixed model. When the advantages of parallel straight line balancing concept are taken into account the idea of the paper is good enough but I have two major concerns about the paper. Response 4-Overall: Your comment is acknowledged. Please find below the responses to your concerns.. rP Fo. Comment 4-1: The authors say in Section 4.3 that: "At the beginning of the assignment procedure (when the final assignment configuration is not known), the most challenging issue is the lack of knowledge on which model will appear in workstations located at the back of the line since the total number of workstations is not known. The algorithm overcomes this problem by considering the maximum processing times of the tasks common in different models when assigning a task from the back of the line (or precedence relationships diagram)." Considering the maximum processing time of a task is not an appropriate approach to overcome the problem of model mix combinations in the workstations. For example if we look at the Figure 2 (The changing model combinations through different production cycles) we see that model mix combinations of (E,E) and (D,D) will occur in the first crossover workstation of Line II. The remaining model mix combinations of (D,E) or (E,D) will never occur in such an assignment. Let’s say that these workstation‐task assignments shown in Figure 2 are the best assignments for the problem. Now suppose that the first task in the precedence diagram of Line II requires 5 minutes for model D and 3 minutes for model E. Similarly the last task of the precedence diagram requires 5 minutes for model D and 6 minutes for model E. Then consider the cycle time is 10 minutes. In such a situation, we cannot able to assign the first and the last tasks of Line II to a crossover workstation because in the case of model D appears in the front side of the line we take into account the actual processing time of the first task for model D (5 minutes) and the maximum processing time of the last task (6 minutes). The total processing time of these two tasks will be 11 minutes and will exceed the cycle time. Thus we miss the opportunity of achieving the assignment shown in Figure 2. Actually, the assignment shown in Figure 2 is a feasible assignment because as I explained above only two model mix combinations (E,E) and (D,D) will occur in related workstation and total processing time of the first and the last tasks does not exceed the cycle time for both of these combinations. But it will be missed by the reason of considering maximum of the processing times of a task common in different models. The assignment results which are missed in this manner are able to be better results compared to obtained ones. This is the most important weakness of the solution approach presented in the paper. Response 4-1: Your comment is appreciated. The main advantage of a U-line system is the opportunity to start assigning tasks from both front and back of the precedence relationships diagram, simultaneously. This works perfectly in single-model U-lines. However, in mixed-model U-lines, the processing time of a task may show difference from one model to another, as you mentioned. Therefore, to satisfy the capacity constraint when assigning a task, it must be known which model to appear in each workstation located at the back of the line. However, this is challenging as the number of stations is not known until all tasks have been assigned.. w. ie. ev. rR. ee. ly. On. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(6) International Journal of Production Research. When assigning a task from the back of the line, the algorithm proposed here considers the maximum processing time of a task common between product models. As you exemplified, it is obvious that some assignment solutions to be missed in this manner are able to be better results compared to obtained ones. That is why the algorithm proposed here handles not only the line balancing problem but also the model sequencing problem, as explained in the same section (Section 4.3). Thus, the combinations of models are changed by the algorithm during the assignment procedure to be able to obtain better assignment solutions. Furthermore, the paper contributes to knowledge by not only proposing a new and comprehensive algorithm but also introducing an innovative assembly line concept, MPUL. The authors believe in that a possible drawback that may be caused by the proposed algorithm due to the sophistication of the problem should not shade the success of the line concept proposed. Comment 4-2: I see that walking times operators in crossover and common workstation are ignored in the paper. The line layout which is called as parallel U‐shaped lines by the authors has been addressed as “embedded U‐lines” in the study of Miltenburg. (Miltenburg, J., 2001, U‐shaped production lines: A review of theory and practice, International Journal of Production Economics, 70 (3), 201‐214.) (Figure 2C). Miltenburg says in the mentioned study that “The embedded U‐line arrangement in Fig. 2C has a large U‐line encircling a small U‐line, all manned by two operators. This is the least common complex U‐line, because it may take up a lot of space and so require a lot of walking.” In the light of this information I think ignoring the walking times of operators in common and crossover workstations is not an appropriate approach for practice in such a line layout. Response 4-2: Thank you for your comment and addressing to this valuable research, Miltenburg (2001). There are three major differences between our concept and that of Miltenburg (2001). To make a direct comparison, the “embedded U-line arrangement” presented in Miltenburg (2001) is given in Fig. 2 and the mixed-model parallel U-line concept proposed in our study is given in Fig. 3.. w. ie. ev. rR. ee. rP Fo. Fig. 2 (Miltenburg (2001)).. On. Fig. 3 (current work).. •. First of all, as clearly seen from Fig. 2 and understood from the statement of “The embedded U‐line arrangement in Fig. 2 has a large U‐line encircling a small U‐line, all manned by two operators…” given in Miltenburg (2001), the whole system is operated by only two operators. This requires operators walk quite a long distance across the line from one workstation to another. However, in our concept, each operator is only responsible with one workstation utilised in only one line – called regular stations, or between the opposite areas of two lines – called multi-line stations (or branches – called crossover workstations). You will notice 17 workstations (which equivalents to 17 operators) in Fig. 3.. •. Secondly, the inner line (small U-line as called in the study of Miltenburg (2001)) shown in Fig. 2 does not allow operators work between its two (front and back) branches. This requires other operators (who work between Line-A and Line-B) constantly travel back and forth between the two lines to complete all tasks.. •. Finally, as mentioned in Miltenburg (2001), “A bigger disadvantage (of the embedded U‐line arrangement) is that the same operator is usually not able to operate the entrance and exit operations of a line”. This is caused by the different movement direction of lines in. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 4 of 37. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(7) Page 5 of 37. embedded U‐line arrangement (see Fig. 2). Nevertheless, in our model, the lines move in the same direction. Therefore, the same operator operates on either the entrance of both lines or the exit of both lines. Consequently, the walking distance in our system is much smaller than of that required in embedded U‐line arrangement. Of course walking times are worth to investigating in crossover and common workstations to reflect real-life conditions and make the concept even more practical. However, including such a constraint to an already complex problem at this stage makes it even harder to solve. This has also been explained in the last paragraph of Section 3.. w. ie. ev. rR. ee. rP Fo ly. On. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(8) International Journal of Production Research. Balancing of mixed-model parallel U-shaped assembly lines considering model sequences Ibrahim Kucukkoc a b *, David Z. Zhang a c a. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, England, UK b. c. Department of Industrial Engineering, Balikesir University, Balikesir, Turkey. rP Fo. State Key Laboratory on Mechanical Transmission, Chongqing University, Chongqing, China. Abstract. As a consequence of increasing interests in customised products, mixed-model lines have become the most significant components of today’s manufacturing systems to. ee. meet surging consumer demand. Also, U-shaped assembly lines have been shown as the intelligent way of producing homogeneous products in large quantities by reducing. rR. the workforce need thanks to the crossover workstations. As an innovative idea, we address the mixed-model parallel U-shaped assembly line design which combines the flexibility of mixed-model lines with the efficiency of U-shaped lines and parallel lines. The multi-line stations utilised in between two adjacent lines provide extra. ev. efficiency with the opportunity of assigning tasks into workstations in different combinations. The new line configuration is defined and characterised in details and its. ie. advantages are explained. A heuristic solution approach is proposed for solving the problem. The proposed approach considers the model sequences on the lines and seeks. w. efficient balancing solutions for their different combinations. An explanatory example is also provided to show the sophisticated structure of the studied problem and explain. On. the running mechanism of the proposed approach. The results of the experimental tests and their statistical analysis indicated that the proposed line design requires fewer number of workstations in comparison with independently balanced mixed-model U-. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 6 of 37. lines.. Keywords: Assembly line balancing; design of production systems; production planning; U-shaped assembly lines; mixed-model assembly lines.. * Corresponding author. Email: i.kucukkoc@exeter.ac.uk, ikucukkoc@balikesir.edu.tr, Tel: +441392723613. Contact details for co-author (D.Z.Z), Email: d.z.zhang@exeter.ac.uk , Tel: +441392723641.. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(9) Page 7 of 37. Balancing of mixed-model parallel U-shaped assembly lines considering model sequences Abstract As a consequence of increasing interests in customised products, mixed-model lines have become the most significant components of today’s manufacturing systems to meet surging consumer demand. Also, U-shaped assembly lines have been shown as. rP Fo. the intelligent way of producing homogeneous products in large quantities by reducing the workforce need thanks to the crossover workstations. As an innovative idea, we address the mixed-model parallel U-shaped assembly line design which combines the flexibility of mixed-model lines with the efficiency of U-shaped lines and parallel lines. The multi-line stations utilised in between two adjacent lines provide extra efficiency with the opportunity of assigning tasks into workstations in different. ee. combinations. The new line configuration is defined and characterised in details and its advantages are explained. A heuristic solution approach is proposed for solving the. rR. problem. The proposed approach considers the model sequences on the lines and seeks efficient balancing solutions for their different combinations. An explanatory example is also provided to show the sophisticated structure of the studied problem and explain. ev. the running mechanism of the proposed approach. The results of the experimental tests and their statistical analysis indicated that the proposed line design requires fewer number of workstations in comparison with independently balanced mixed-model U-. ie. lines.. w. Keywords: Assembly line balancing; design of production systems; production planning; U-shaped assembly lines; mixed-model assembly lines.. 1. Introduction. ly. On. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. The manufacturing industry has experienced crucial changes with the industrial revolution emerged in 18th century in England. Mass production techniques have been put into practice by companies to increase capacity and so productivity. Following these developments, which built a base for today’s high-performance manufacturing systems, the first moving-belt was constructed by Henry Ford and his colleagues in early 20th century at Highland Park assembly plant. This was the pioneering attempt to establish an assembly line, which builds the major and the most significant parts of modern production systems in several industries, e.g., automotive, electronics, home appliances etc. (Kucukkoc et al. 2015).. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(10) International Journal of Production Research. An assembly line is a sequence of workstations linked to each other by a conveyor or moving belt, on which homogeneous products are consecutively assembled in an efficient way. The problem of determining which task will be assembled in which workstation with the aim of minimising the total number of workstations and/or cycle time is called the assembly line balancing problem. Some constraints must be satisfied to obtain a feasible line balance, such as capacity constraint, precedence relationships constraint, task assignment constraint, etc. (Kucukkoc and Zhang 2015e). The assembly line balancing problem was first studied by Salveson (1955) in its simplest version (where a simple straight line was considered with a. rP Fo. single commodity of product on the line) and has gained continuing interest from academics as well as practitioners since then. In its traditional version, assembly lines have a straight structure on which a series of workstations are located sequentially, to produce only one type of product in large quantities. The problem of balancing such lines is called simple assembly line balancing problem, which is. ee. an NP-hard combinatorial optimisation problem, as shown by Wee and Magazine (1982). However, as shown by Thomopoulos (1967) and several studies following this, mixed-model lines (where more than one model of a base product are assembled on the same line) carry. rR. several practical advantages over single-model lines. This paper contributes to knowledge by presenting the first and original research results on. ev. mixed-model parallel U-shaped assembly line (MPUL shortly) concept, which was recently introduced by Kucukkoc and Zhang (2015e). So that, as an innovative approach, the model variation flexibility is introduced to the parallel U-shaped assembly line system with the aim of. ie. obtaining well-balanced line configurations by reducing idle times. The addressed line system. w. combines the advantages of its sub-configurations, i.e., mixed-model lines, parallel lines and Ushaped lines as will be explained in the following sections. Thanks to the proposed design, the multi-line stations and crossover stations are of the key factors which provide advantages. As. On. the leading car manufacturers set new goals for advanced flexible manufacturing systems (see for example Ford Motor Company (2015)), which can easily adapt to varying customer demand,. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 8 of 37. the proposed MPUL system can replace the conventional line configurations. Thus, the MPUL system can play crucial roles in “giving customers the features, fuel efficiency and technology they want anywhere in the world” as stated by Ford Motor Company (2015). To solve the balancing problem on MPULs and handle its complexity, which will increase to a great extent due to the contained line configurations which are already complex alone, a heuristic solution approach is also proposed and explained, as another contribution of this research. The remainder of this paper is organised as follows. Section 2 reports the review of literature while Section 3 introduces and defines the proposed MPUL system in details. Section 4 proposes a possible heuristic solution approach for the MPUL balancing problem and explains. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(11) Page 9 of 37. its running principles. Section 5 presents an explanatory example and exhibits the running principle of the heuristic algorithm. The sophisticated structure of the problem and challenging issues are also discussed in the same section. The results of the experimental tests are reported in Section 6 and the conclusions and possible industrial implications of the work are given in Section 7 followed by the future research directions.. 2. Related work During the last six decades, various types of line configurations along with several objectives. rP Fo. and constraints have been studied by academics and practitioners. Thomopoulos (1967) proposed a mixed-model assembly line system, where a variety of product models having similar product characteristics are assembled. Mixed-model lines provide advantages over single-model lines as a variety of similar products can be assembled on the same line with no need of setup times between model changes (Kucukkoc, Karaoglan, and Yaman 2013).. ee. Assembly lines can be divided into two main groups in terms of the line shape: straight lines and U-shaped lines (Miltenburg and Wijngaard 1994). In U-shaped lines (or U-lines, shortly),. rR. the entrance and the exit of the line system are very close to each other. Operators may handle work-pieces both on the front and back of the line thanks to the formed U-shaped line configuration. Operators located in crossover workstations can perform tasks from both front. ev. and back of the line. Thus, idle times are reduced and resource utilisation is increased thanks to the crossover stations located in between front and back of the U-line. Miltenburg and Wijngaard (1994) introduced the U-line balancing problem and a series of researchers followed. ie. them; e.g., see Urban (1998), Scholl and Klein (1999), and Urban and Chiang (2006) for exact. w. solution approaches; Erel et al. (2001), Gökçen et al. (2005), Hwang et al. (2008) and Sabuncuoglu et al. (2009) for heuristic/meta-heuristic solution approaches on simple U-line configurations. Miltenburg (2001) also introduced the embedded U-line arrangement, which. On. considers “a large U-line encircling a small U-line, all manned by two operators”. The difference between the embedded U-line arrangement (Miltenburg 2001) and the MPUL concept described in the current work will be provided in Section 3.. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. Almost decade ago, Gökçen et al. (2006) introduced the line parallelisation idea to minimise idle times by maximising the use of shared resources. Parallel line configuration provides the opportunity of building multi-line stations in which operators can perform jobs from both of the adjacent lines. This also helps obtain well-balanced line configurations as there is more chance to assign tasks in different combinations. The line parallelisation idea has been applied to mixed-model lines, where more than one model of a base product is assembled on the same line, by Ozcan et al. (2010). Ozcan et al. (2010) introduced the parallel mixed-model line system and demonstrated. the. requirement. of. considering. balancing. and. sequencing. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk. problems.

(12) International Journal of Production Research. simultaneously on those lines through experimental tests. In another study, Ozcan et al. (2010) located more than one two-sided line in parallel to each other and introduced the parallel twosided assembly line system. A tabu search approach was also developed to find efficient solutions for the parallel two-sided assembly line balancing problem. Kucukkoc and Zhang (2015c, 2015d) developed a genetic algorithm approach and an ant colony optimisation based approach for solving the parallel two-sided assembly line balancing problem with different objectives. Kucukkoc and Zhang (2014b, 2014a) improved the parallel two-sided assembly line system in a mixed-model production environment and proposed agent-based ant colony. rP Fo. algorithms for solving the problem efficiently. In their latter study, Kucukkoc and Zhang (2015b) enhanced the agent-based ant colony optimisation algorithm by integrating a genetic algorithm based model sequencing mechanism. As the common consequence of these researches, it was shown that locating two lines in parallel to each other helps minimise the total number of workstations.. ee. As the pioneering research in parallelisation of the U-shaped lines, the study by Kucukkoc and Zhang (2015a) introduced the parallel U-shaped assembly line system. However, model variations across the lines have not been considered in their study. Instead, a single product. rR. model is produced on each of the U-shaped lines located in parallel to each other. Mixed-model production have been extensively studied on individual U-shaped lines. Sparling and Miltenburg (1998) introduced the mixed-model U-line (MMUL) balancing problem and. ev. presented an approximate solution approach with a numerical example. The model sequencing problem was not considered in their research. Kim et al. (2006), developed a new genetic. ie. approach, called endosymbiotic evolutionary algorithm, to deal with both balancing and sequencing problems in MMULs. Kara et al. (2007), presented a multi-objective approach. w. (enhanced with a neighbourhood generation method) for solving the same problem with the aim of minimizing the absolute deviations of workloads, part usage rate and cost of setups. Özcan et. On. al. (2011), Kazemi et al. (2011) and Hamzadayi and Yildiz (2012) developed genetic algorithm based approaches for balancing and sequencing MMULs. While Özcan et al. (2011) considered the stochastic task processing times, Kazemi et al. (2011) allowed the assignment of common. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 10 of 37. tasks into different stations. Parallel workstations and zoning constraints were considered in Hamzadayi and Yildiz (2012). Hamzadayi and Yildiz (2013) and Kara (2008) proposed simulated annealing algorithms for balancing and sequencing MMULs. In a latter study, Kara and Tekin (2009) presented a mixed integer programming formulation which minimises the number of workstations for a given model sequence. Lian et al. (2012) developed a modified colonial competitive algorithm for solving the line balancing and model sequencing problems in MMULs simultaneously. The objective was to minimise the absolute deviations of workloads. The performance of the algorithm was compared with that of existing algorithms through test. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(13) Page 11 of 37. problems. Li et al. (2012) studied the problem of sequencing minimum product sets in MMUL. While the line balancing problem was not considered in their research, a branch and bound algorithm was proposed to minimise the work overload. Rabbani et al. (2012) addressed the mixed-model two-sided assembly lines in a multiple U-shaped layout environment. A mixedinteger programming formulation and a genetic algorithm based heuristic were developed to simultaneously minimize the cycle time and the number of workstations. In another study, Rabbani et al. (2012) considered only the line balancing problem on MMULs and presented a genetic algorithm approach with the aim of minimising crossover workstations considering. rP Fo. operator travel times. Manavizadeh et al. (2013) developed a simulated annealing approach which assigns operators with different skill levels into workstations upon the line balance is obtained. Another simulated annealing approach was developed by Dong et al. (2014) to minimise the expectation of work overload time when balancing and sequencing MMULs. For the same problem, Manavizadeh et al. (2015) developed a multi-objective heuristic algorithm which incorporates the minimization of the cycle time, the wastages in each station and the. ee. work overload. Kucukkoc and Zhang (2015e) introduced the MPUL concept, where the variants of a base product can be assembled on each of the parallel U-lines in different model mixes.. rR. As seen from this comprehensive survey, only the study by Kucukkoc and Zhang (2015e) incorporated model variations on parallel U-shaped lines. Kucukkoc and Zhang (2015e) brought the MPUL idea to the attention of academia. However, no solution method was proposed in. ev. their study. Also, they have not presented research results, which prove the advantages of MPULs over conventional (or independently balanced) MMULs. As a continuing research built. ie. over Kucukkoc and Zhang (2015e), this paper fills in this gap through presenting new and original research results obtained from a new solution method developed for MPULs. The. w. individual model sequences of the lines have been considered to prevent infeasible solutions and violation of capacity limits. Furthermore, a paired-sample t-test was conducted to statistically. On. prove the advantage of MPUL over independently balanced MMULs.. 3. Problem description 3.1. Main characteristics and advantages. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. The parallel U-shaped assembly line system is a combination of two or more U-shaped assembly lines, represented by (ℎ = 1, … , ), located in parallel to each other. Two or more different product models, where each model on is represented by

(14) ( = 1, … , ), are produced on each of the U-shaped assembly lines. Each product model produced on each of the lines has its own set of tasks, where a task is represented by ( = 1, … , ), performed according to predefined precedence relationships. represents the set of predecessors of task. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(15) International Journal of Production Research. for model

(16) . Each task ( ) for model

(17) on line requires a certain amount of processing time, symbolised with , to be performed. In such a parallel U-shaped assembly line system, operators located in between two adjacent U-lines will have the opportunity of performing their jobs on both of the lines. Meanwhile, operators located in the centre of the inner U-shaped line will have the flexibility of performing tasks on the front and back of the line. The proposed parallel U-shaped assembly line system is illustrated in Figure 1. -------------------------------------Figure 1. The proposed parallel U-shaped assembly line system.. rP Fo. --------------------------------------. As it can be seen from Figure 1, two U-shaped lines are located in parallel to each other. Operators located in multi-line stations are allowed to perform their jobs belonging to the models assembled on both Line-I and Line-II. This brings the opportunity of assigning tasks to the workstations in different combinations. By this way, the idle times of workstations are. ee. reduced (therefore the efficiency of the whole line system is increased) as well as the communication between workers is increased. It is also possible to utilise regular workstations. rR. instead of multi-line stations depending on the overall efficiency of the line configuration obtained.. The proposed system also carries the advantages of U-shaped lines as crossover stations are. ev. allowed to be utilised in the centre of the inner line. The operators located in these workstations can travel between the front and back of the line to help perform jobs on both branches of the U-. ie. line. Also, there are regular stations in which tasks from only one branch of the line are accomplished.. w. As an advantage of the proposed assembly line system, each of the parallel lines may have a different cycle time regardless of the other one. On one hand, this increases the flexibility of the. On. system because it is possible to produce products in different throughput rates. On the other hand, the complexity of the problem of balancing this line system increases as it is needed to determine common time slots between the two lines to be able to assign tasks in multi-line. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 12 of 37. stations. Gökçen et al. (2006) used least common multiple (LCM) based approach to make modelling easier when different cycle times are subject to consideration in such a parallel line system configuration (Zhang and Kucukkoc 2013; Kucukkoc and Zhang 2014c). This procedure will not be repeated here due to page limit. The MPUL concept differs from the embedded U-line arrangement addressed in Miltenburg (2001) in three ways. First of all, in embedded U-line arrangement, the whole system is operated by only two operators. This requires operators walk quite a long distance across the line. However, in our concept, each operator is only responsible with one workstation utilised in. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(18) Page 13 of 37. only one line – called regular stations, or between the opposite areas of two lines – called multiline stations (or branches – called crossover workstations). Secondly, the inner line (small Uline as called in the study of Miltenburg (2001)) does not allow operators work between its two (front and back) branches. This requires other operators constantly travel back and forth between the two lines to complete all tasks. Finally, as mentioned in Miltenburg (2001), “A bigger disadvantage (of the embedded U‐line arrangement) is that the same operator is usually not able to operate the entrance and exit operations of a line”. This is caused by the different movement direction of lines in embedded U‐line arrangement. Nevertheless, in our model, the. rP Fo. lines move in the same direction. Therefore, the same worker operates on either the entrance of both lines or the exit of both lines. 3.2. Challenging issues. On two-sided assembly lines, where both sides of the line (called left and right sides) are used,. ee. some tasks can be performed on the left side of the line while some tasks belonging to the same model can be performed on the opposite (right) side of the line. There may be precedence relationships between those tasks performed on the opposite sides of the lines. This. rR. phenomenon is called interference and extra attention is needed to avoid violation of precedence relationships as this may cause infeasible solutions. In the line system proposed in this research, the situation is similar to the two-sided lines because it is allowed to perform jobs on both sides. ev. of the Line-II (see Figure 1). When a model belonging to Line-II is being assembled, two different operators – one in the multi-line station between two adjacent lines while the other one. ie. is in crossover station or regular station in the centre of Line-II – can work on the same workpiece. The challenge in this situation is to ensure precedence relationships among tasks caused by technological or organisational requirements.. w. Capacity constraint is another must have requirement that needs to be satisfied in assembly line. On. balancing problems. Each workstation has a limited time, called cycle time, in which they need to complete their tasks. In a paced (synchronous) assembly line, all workstations are linked to. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. each other via a conveyor or any other transportation system. The synchronisation is achieved by transferring semi-finished product models between stations at a pre-determined and fixed time interval. In the proposed line system, each workstation utilised on the same line has the same capacity, irrespectively whether or not it is a multi-line station. The capacity of a multiline station is determined by the cycle time of the line on which the multi-line station is constructed. Crossover stations and regular stations adhere to the cycle time of Line-II. Obviously, when an LCM based approach is applied, both lines will be balanced using the same cycle time (but modified task times) and this makes modelling and solving the problem easier.. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(19) International Journal of Production Research. In some cases, there can be other constraints caused by the safety rules or allocations of the workstations, such as positive-negative zoning constraints and positional constraints. The positive zoning constraint requires the two tasks be assigned in the same workstation while in the negative zoning constraint two tasks must be assigned in different workstations. Also, in some situations, a certain task may need to be operated at a certain workstation. This is assured by positional constraints. 3.3. Model changes. rP Fo. Introducing the product model diversity to such a complex production environment makes modelling and solving the problem harder to a great extent. The most important factor that contributes to this complexity is the change in product models on the parallel lines from one production cycle to another. A production cycle is defined as a phase of the line system where there is a different mix of products in the workstations. When the cycle times of the parallel. ee. lines are different, model changes on the lines will take place at different times and this yields a quite complex situation to manage in multi-line stations. The total number of different production cycles that can appear in a parallel assembly line system depends on the product mix. rR. assembled on the lines. Formulations on how to calculate production cycles will be provided in Section 4.. ev. To give an example, let us assume a parallel U-shaped assembly line system composed of two lines, Line-I and Line-II, where a mix of different product models are assembled on each of the U-lines, i.e., models A, B, and C on Line-I and models D and E on Line-II. The cycle times of. ie. Line-I and Line-II are 10 time-units and 20 time-units, respectively. Therefore, the moving. w. speed of Line-I is as double of that of the Line-II. If the model sequences on Line-I and Line-II are considered as = and = , possible production cycles will be as in Figure 2. --------------------------------------. On. Figure 2. The changing model combinations through different production cycles.. --------------------------------------. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 14 of 37. To identify workstations (symbolised with ! ), the working space is divided into different zones (" = 1,2, … ,4) and queues (% = 1,2, … , &; where & = 6 in this example) as seen from Figure 2. The workstations located in between two adjacent lines and assigned tasks from both of the lines are called multi-line stations (e.g., see , ( , ) , etc.) and operators located in these workstations can perform their jobs on both of the lines. Workstations located in between the front and back branches of Line-II and assigned tasks from both branches are called crossover stations (e.g., and * ) and operators located in these stations can perform. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(20) Page 15 of 37. their jobs on either branch. As in traditional configurations, regular stations (e.g., and ( ), in which operators perform their jobs for only one specific line and/or branch are also allowed.. 4. Mixed-model parallel U-line heuristic (MPUH) This section proposes a heuristic algorithm to find balancing solutions for the MPUL system introduced in the previous section.. rP Fo. 4.1. Pseudo-code of MPUH. The heuristic procedure proposed by Kucukkoc and Zhang (2015a) for parallel U-line systems has been improved and adapted for the MPULs. Thus, the algorithm proposed in this paper, called mixed-model parallel U-line heuristic (or MPUH shortly), integrates the modifications of two well-known heuristics, the ranked positional weight method (Helgeson and Birnie 1961). ee. and the maximum number of successors (modified from Tonge (1960)), in an MPUL production environment. The main aim is to minimise the number of workstations as a primary goal and to. rR. minimise the line length (or the number of queues) as an additional goal. Therefore, if two solutions, which has the same number of workstations but different lengths are obtained, the one with the lower length is preferred. As the MPUL system is a much more complex problem in. ev. comparison with its single-model version, it requires an even more sophisticated solution procedure to obtain efficient balancing solutions. Therefore, the MPUH procedure, which uses a ,) value for selecting tasks, comprises several newly introduced task priority index (+. ie. improvements as the details will be explained in this section. The superscript “PI” is used here. w. ,as an acronym for priority index. The task priority index (+ ) of a task is the multiplication of. ,. /0 ,its positional weight index (+ ) and the number of successors index (+ ); i.e., + =. ,. ,. /0 + × + . In this equation, the positional weight index (+ ) of a task is determined by its. On. positional weight ( ) which is calculated as follows; = 2 + ∑ ∈067 2 , where represents the set of successors of task on line . The term 2 denotes the :. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. :. 6 6 weighted processing time of task and is calculated as 2 = 8∑ ; 9 < =∑ ; 9. where ℎ = 1, … , ; = 1, … , (to recapitulate, is the processing time of task ). Afterwards, on each of the lines, the tasks are sequenced in descending order based on their ,. values and the positional weight index (+ ) of the task which has the lowest value ,. is set to ‘1’. The + value of the task which has the second lowest value is set to 2 and ,. this is repeated until every task is assigned a + value. If there are two or more tasks which. have the same positional weights, the lowest numbered task gets the higher positional weight index.. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(21) International Journal of Production Research. /0 To calculate the number of successors index (+ ) of a task, the total number of successors. (> ) of this task is calculated as > = ?@A9B C, where ?@A9B C corresponds to the. length of the set of successors of task on line . On each of the lines, tasks are sequenced in /0 descending order based on their > values and the + value of the task which has the lowest /0 value of the task which has the second lowest > value is > value is set to ‘1’. The +. assigned 2, and so on. These calculations will be exemplified in Section 5. The pseudo-code of the proposed MPUH procedure is given in Figure 3.. rP Fo. -------------------------------------Figure 3. The pseudo-code of MPUH.. --------------------------------------. 4.2. Diversification. ee. A stochastic assignment procedure is applied in MPUH to alternate assignment positions during the balancing process and have more diversified as well as efficient balancing solutions. For this aim, depending on the value of a newly introduced random boolean variable (DEAFGAH@),. rR. the value of " index is randomly determined after a new task is assigned. Thus, for example, if the assignment procedure is being performed on the front area of the line system (DEAFGAH@ = AIH), " is randomly assigned 1 or 2 (" = A@G9F

(22) JGHKHAH2HHG[1,2]).. ev. When there is no available task for the current assignment area (front or back), the value of DEAFGAH@ is alternated (DEAFGAH@ = N@ODH), and " is assigned a random value. ie. depending on the value of DEAFGAH@ as exemplified in the pseudo-code. 4.3. MPS principle. w. At the beginning of the assignment procedure (when the final assignment configuration is not. On. known), the most challenging issue is the lack of knowledge on which model will appear in workstations located at the back of the line since the total number of workstations is not known. The algorithm overcomes this problem by considering the maximum processing times of the. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 16 of 37. tasks common in different models when assigning a task from the back of the line (or precedence relationships diagram). For this aim, a newly introduced term, namely deserved task time ( ), is used as will be explained below. When assigning tasks to the front areas of the lines, the task processing times belonging to the actual models are used by the algorithm, as different from the back of the line. The algorithm generates possible model sequences and the minimum part set (MPS) principle (Bard, Darel, and Shtub 1992) is used to determine model mixes on the lines. The MPS approach was used by Ozcan et al. (2010) for parallel mixed-model lines and Kucukkoc and Zhang (2014a) for mixed-. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(23) Page 17 of 37. model parallel two-sided lines. The (ℎ = 1, … , ) is a vector which represents the smallest set having the same proportions of different product models as the demands. It represents the mix of product models on line , such that = (9 , … , 9:6 ), where 9 = ⁄K?9 (where = 1, … , and ℎ = 1, … , ). The denotes the demand of model

(24) ( = 1, … , ) on (ℎ = 1, … , ). The K?9 (ℎ = 1, … , ) is the greatest common divisor of the demands of the product models assembled on the same line ( , where ℎ = 1, … , ). Obviously, the total demand is met by K?9 times repetition of producing the . The model sequence of line is represented with and the length of for one ,. rP Fo. which means the total number of products on line for one , is calculated as follows; :. 6 = ∑ ; 9 . Thus, the maximum number of different model combinations for a determined. model sequence pattern on two lines is calculated as QRS = ( × ). This also regulates how many different production cycles (T = 1, … , U) the system should be split into (U = QRS ) (Ozcan et al. 2010).. ee. 4.4. Complex task selection procedure. rR. The list of available tasks on (where ℎ = 1, … , ) is symbolised with . When determining available tasks, the tasks in the unassigned task lists for Line-I and Line-II (V and V ) are checked one-by-one. If a task being checked (called a candidate task) is from the. ev. front of the precedence relationships graph, either the task should have no predecessors or all of its predecessors (if any) must have been assigned and completed. However, if the task is from. ie. the back of the precedence relationships graph, either the task should have no successors or all of its successors (if any) must have been assigned and completed. Also, the remaining capacity. w. in the current workstation should be large enough to perform the task. To determine whether there is enough capacity, there are three important components which need to be considered: (i). On. the workload of the current workstation, (ii) the earliest starting time of the candidate task, and (iii) the deserved task time ( ) of the candidate task. The is a newly introduced term for MPUL system, because, at the beginning of the balancing process (when the final balance and. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. so the total number of workstations are uncertain), it is not known which model will appear at the back of the line (i.e., Line-I back and Line-II back). Due to this uncertainty, the maximum processing time of the candidate task among different models being produced on the same line will be considered when assigning a task from the back of the line, ← maxQ6[∈:6 \ ]. However, as it is known which model will appear on the front of the lines, the task processing time of the relevant model will be used when assigning a task from the front of the precedence relationships graph, ← . Therefore, the capacity constraint will be satisfied by task `. `. if the following condition is fulfilled: ≥ +

(25) @_\ ! , ] for all production. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(26) International Journal of Production Research. `. cycles. The term corresponds to the earliest starting time of task in production cycle T and is determined by the latest completion time of its predecessors (if the task is from the front of the line) or successors (if the task is from the back of the line). When selecting and assigning tasks to workstations, the task which has the best priority index ,,(+ ) value is preferred. However, the best + depends on the position of the available task. If. the task is from the front of the precedence relationships graph (regardless of Line-I or Line-II), ,then the best priority index corresponds to the maximum + . On the other hand, if the task is. from the back of the precedence relationships graph (regardless of Line-I or Line-II), the best. rP Fo. ,. priority index corresponds to the minimum +. To increase the diversity of the solutions obtained and scan the search space more effectively, randomness is allowed when selecting tasks. Randomness is a commonly applied technique in assembly line balancing approaches, especially in priority rule-based methods, and as mentioned by Otto and Otto (2014), the quality of the solutions obtained by such methods can. ee. be improved by “applying several passes of this priority rule with some kind of random influence”. For this aim, a random number, A ∈ (0,1), is determined by the algorithm. If. rR. A ≤ cJ, where cJ ∈ [0,1] is the randomness index and determined by the user at the beginning, a random task is selected among the available ones. If A > cJ, then the task which has the best ,+ value among the available tasks is selected. Another randomly determined number,. ev. A ∈ (0,1), is used to decide on the list from which the task will be picked, i.e., or . If A ≤ 0.5, the task is tried to be selected from . If A > 0.5, the algorithm tries to assign a. ie. task from . If any of the lists is empty, then the task is picked from the other list. When a. task ( ) is assigned to a workstation ( ! ) on line ( ), its workload time is increased by. w. `. `. +

(27) @_\ ! ` , ] for all production cycles, ! ` ← +

(28) @_\ ! ` , ] where T = 1, … , U.. On. `. is also used when updating values of tasks. If the task is assigned from the front of `. the precedence relationships graph, then values of its successors will be set to + `. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 18 of 37.

(29) @_\ ! ` , ]. On the contrary, if the task is assigned from the back of the precedence. relationships. graph,. +

(30) @_\. !`. then. ` , ].. `. . values. of. its. predecessors. will. be. set. to. 5. An explanatory example A small-scale numerical example is given here to show the sophisticated structure of the MPUL balancing problem and the running principle of MPUH, explicitly.. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(31) Page 19 of 37. 5.1. Problem data Let us consider two U-shaped lines, Line-I and Line-II, located in parallel to each other, as in the example given in Section 3. Two different sets of models are produced on each of the parallel lines, i.e., models A and B on Line-I, and models C and D on Line-II. A common precedence relationships diagram is built among tasks belonging to the models produced on each of the parallel lines. The processing times of tasks and the precedence relationships are given in Table 1. The IM column presents the immediate successor(s) of the corresponding task. The model demands are assumed g = 24, h = 72, j = 48 and l = 48 for a planning. rP Fo. horizon of 960 time-units. Thus, the cycle times of the lines are simply calculated as = = 10 time-units. When the MPS principle explained in Section 4 is applied, the model mixes on Line-I and Line-II are obtained as 9 = (1,3) and 9 = (1,1), respectively, which means = 4 and = 2. This leads to a maximum of U = QRS = 8 different production cycles on the lines.. ee. --------------------------------------. Table 1. Input data for the numerical example (task times in time units).. rR. -------------------------------------5.2. Steps of MPUH. ev. Table 2 shows the task selection principle of MPUH through an example solution for the. ie. problem given. Note that only the first 14 steps are provided due to page limit. The task selected from the list of available tasks at each step, and the completion time of the selected task for each. w. production cycle can be seen from the table. In the Completion Time column, the models that will appear in workstations located at the front of the line are also given in brackets. As the. On. specific models that will appear in workstations located at the back of the line are unknown, they are marked with ‘[M]’. In this situation, the maximum task processing time among all models on the same line is considered (as explained in Section 4). Model sequences are assumed = BC and = BC. --------------------------------------. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. Table 2. The task selection procedure.. -------------------------------------As seen from Table 2, the assignment procedure starts from the front area of Line-II (" = 2, % = 1). Amongst the available tasks from Line-I and Line-II, the algorithm selects task 2 ∈ , , which has the maximum + value among the tasks on Line-II, to assign in workstation. . The completion times in this workstation are updated as 2, 5, 2 and 5 for production. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(32) International Journal of Production Research. cycles 1, 2, 3 and 4, respectively. The earliest starting times of the successors of task 2 on LineII are also updated for each production cycle. In the next step (step 2), z is assigned 1 (" = 1) and task 1 ∈ is assigned to workstation . The completion times and earliest starting times are updated and this cycle continues until there is no available task for this queue. The algorithm proceeds to the next queue in step 12. In step 14, task 5 ∈ is assigned to the. multi-line station utilised on Line-I ( ). The operator allocated in operates on both lines, i.e., he/she performs operations for models A and B being assembled on Line-I and. models C and D being assembled on Line-II. As seen from the table, no crossover station is. rP Fo. utilised in the first 14 steps provided. The algorithm consecutively determines which product model will appear on the front of the line as the new queue is utilised based on the model sequence given ( = BC and = BC). However, the final configuration of product models, including the back of the lines, is achieved once all the tasks have been assigned and so the total number of workstations. ee. has been determined. In such an environment where it is not known which model will exist in the back of the line, it is not easy to assign tasks to the workstations by ensuring that capacity. rR. constraint is satisfied while pursuing to obtain an efficient line balance. 5.3. Final solution. ev. Figure 4 gives the best balancing solution obtained after MPUH algorithm was run for 50 iterations (

(33) @_@O@G?GKJ>I

(34) oHA = 50). Note that many different solutions may be. ie. obtained during these iterations thanks to the stochastic task assignment procedure of MPUH. The procedure (and the sample task assignments) given in the previous subsection can be. w. followed when building a sample balancing solution in any iteration. However, the best solution obtained eventually (given in Figure 4) is completely different from this sample balancing. On. solution, as expected. As seen from the figure, 10 workstations are constructed; of which four are multi-line stations (i.e., , , ( and (( ), one is crossover station (i.e., ) and. five are regular stations (i.e., ( , * , , ( and ( ). The multi-line stations and. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 20 of 37. crossover stations will be influenced from the model changes during production cycles. This is exhibited in Table 3, in which the final workload times of workstations are reported across four production cycles. In accordance with the number of workstations obtained, possible production cycles are also provided in Table 3. As can be seen from the table, the model type that will exist in the workstations located in the back of the line tightly depends on the total number of workstations utilised across the lines.. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(35) Page 21 of 37. -------------------------------------Figure 4. The best balancing solution obtained after 50 iterations.. -------------------------------------Table 3. The workload times of workstations across production cycles.. -------------------------------------To give an example regarding the workload variations in multi-line stations, let us consider workstation given in Figure 4. In the first production cycle, model B and model C will be. rP Fo. under operation on Line-I and Line-II, respectively. The operator working in this workstation will complete tasks 2 and 6 on model B on Line-I and he/she will then perform task 3 on model C belonging to Line-II. Thus, the workload of this workstation will be 9 time units in production cycle 1. In the next production cycle, the workload of will remain the same although model D will appear on Line-II. This is because both models, C and D, require the same amount. ee. of time for task 3. However, this situation will change in the next production cycle with the launch of models A and C. The workload time of will increase to 10 time units in production cycle 3. In another multi-line station, , the model combinations on Line-I and. rR. Line-II and so workload time of the workstation will change four times; i.e., workload time will be 9, 9, 9 and 10 time units in production cycles 1, 2, 3 and 4, respectively. Similarly, there will be changes in the model combinations in the crossover station, . In production cycles 1 and. ev. 3, models C and D will exist on the front and back of Line-II, respectively, by requiring 8 time units of workload time. In production cycles 2 and 4, models D and C will appear and fill up the capacity of with 10 time units.. w. ie. If these two lines were balanced independently, a total of 11 workstations (i.e., 6 workstations for Line-I and 5 workstations for Line-II) would be needed to perform tasks for all models.. On. Therefore, it is clear that the proposed MPUL design helps save one workstation for this particular case.. 6. Experimental tests. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. As there is no suitable comparable result reported in the literature, to show the practical benefits of the proposed MPUL system, standard test problems have been derived from the literature and solved using the proposed MPUH algorithm under two different conditions: independent balancing (IB) and MPUL. The MPUH algorithm has been coded in Java SE 7u4 environment and run on a PC with 3.1GHz Intel Core™ i5-2400 CPU. A total of 24 test cases have been formed using the test problems, i.e., one test problem on Line-I and another test problem on Line-II. In IB, Line-I and Line-II have been considered as two separate MMUL systems and the two lines were balanced separately such that no multi-line stations were allowed. In MPUL. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(36) International Journal of Production Research. condition, a MPUL system has been established where the two lines were located in parallel to each other, as proposed. Thus, it was aimed to measure the benefit of the proposed MPUL system against existing MMUL system. Based on some preliminary tests, the randomness index parameter is assumed cJ = 0.5 to obtain more diversified solutions, as contextualised in Section 4. The algorithm was run 100, 200 and 300 iterations for test cases 1-6, 7-15 and 16-24, respectively, and the solution which gives the minimum number of workstations (NS) value was taken for each test case. Table 4 presents both the design and the results of the experimental tests. The problems. rP Fo. considered on each line are given in Line-I and Line-II columns for each test case. The cycle times of the lines and the minimum part sets (see MPS column) belonging to the models produced on particular lines are presented in the table. The table comparatively reports the results of test cases solved as well. The IB column reports the sum of the NS values for Line-I and Line-II when the lines were balanced independently. In the MPUL column, the number of. ee. queues (NQ) and the NS values of the obtained solutions are reported for each test case. The Diff column denotes the relative difference in the NS values between the two solution strategies and is calculated as NN = (J/0 − V/0 )/J/0 .. rR. -------------------------------------Table 4. The design and results of experimental tests.. ev. -------------------------------------As can be seen from the results, the proposed MPUL design helps reduce the number of. ie. workstations in 11 out of 24 test cases. The largest difference (0.33 or 33%) was observed for test case 5 for which the IB and MPUL solutions were obtained 6 and 4, respectively. Thus,. w. MPUL system helped save two workstations for this particular case. The second (0.25) and the third (0.17) best improvements have been recorded for test cases 4 and 1, respectively. For test. On. case 4, the proposed MPUL design requires 6 workstations while 8 workstations would be needed when the lines were balanced independently. Hence, a 25% improvement has been achieved. In test case 1, the MPUL design helped save one workstation with a 17 percent. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 22 of 37. improvement over the IB condition. In test cases 13 and 21, two workstations were saved while one workstation was saved in test cases 9, 10, 14, 16, 17 and 22. For the remaining 13 test cases, MPUL heuristic requires the same number of workstations with IB solution. A paired sample t-test was conducted to statistically analyse the experimental test results and determine whether the proposed MPUL system makes a significant improvement over IB. For this aim, the NS values obtained by the two solution strategies were used as input data. The hypotheses stated at the 95% confidence interval (s = 0.05 significance level) are as follows:. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(37) Page 23 of 37. t : There is no statistically significant mean difference in NS values obtained by IB and MPUL (u:,vw = u-h ).. : The mean difference in NS values obtained by IB and MPUL are statistically significant (u:,vw ≠ u-h ). The data was analysed using Minitab 16 statistical software package. The test results presented in Table 5 indicated that there was a significant difference in the mean NS values of MPUL (13.96 ± 7.60) and IB (14.58 ± 7.59); (23) = −3.98, < 0.001. Specifically, these results confirmed that the proposed MPUL system helps minimise the total number of workstations in. rP Fo. comparison with independently balanced MMULs. This has clearly demonstrated that the parallelisation of MMULs provides promising advantages which need further investigation in future studies.. --------------------------------------. ee. Table 5. The paired sample t-test results.. --------------------------------------. rR. 7. Discussion and conclusions. The main aim of this study was to introduce a flexible as well as efficient manufacturing system. ev. design which may replace traditional U-shaped lines, in future. For this aim, two MMULs were located in parallel to each other and a unique line configuration was obtained. So that, tasks. ie. belonging to the models being produced in an inter-mixed sequence on both of the lines can be performed at multi-line stations utilised in between two adjacent lines. Also, as emphasised in. w. details in this paper, the proposed line system combines the advantages of its individual subconfigurations (i.e., mixed-model lines, parallel lines and U-shaped lines) which have already. On. been discussed widely in the literature. The MPUL balancing problem was defined and discussed by taking model sequences into consideration. It was illustratively shown that the feasibility and so the quality of a balancing solution obtained is affected by the sequences of. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. International Journal of Production Research. models being assembled on the lines. The dynamism of model combinations in multi-line stations and crossover stations and their effects on the workload times of these workstations have also been exhibited clearly. In addition to the benefits of the proposed system, such a complex system design brings some difficulties which require sophisticated solution procedures for building efficient balancing techniques. As an advantage of the U-shaped lines, the balancing process starts from both front and back areas of the lines and this provides advantages over straight lines. However, as the number of workstations that need to be utilised is uncertain at the beginning of the balancing process, it is not known which models will appear in the workstations located at the back of the. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.

(38) International Journal of Production Research. line. In this environment, a heuristic algorithm was proposed to generate feasible model sequences considering minimum part sets and build balancing solutions considering these model sequences. An explanatory example has been provided to show the running principle of MPUH and the implementation of the MPUL idea. Experimental tests have also been conducted to examine the superiority of the MPUL design against independently balanced mixed-model lines. The experimental test results and their statistical analysis have confirmed the advantages of the proposed design in minimising the total number of workstations. As a possible industrial. rP Fo. application of the research, the techniques implemented in this study can easily be adopted by practitioners, e.g., line managers in car manufacturing plants, as explained in the paper. By this way, companies will be able to produce customised products designed based on their customers’ requests while reducing the need for workforce.. ee. 8. Future research directions. The outcome of this paper made it clear that the MPUL design has a promising potential to yield. rR. more efficient line systems. Therefore, the implementation of the MPUL idea and the MPUH algorithm can be improved in future studies. Developing an improved procedure to detect which model will be produced on the back of the line at a specific workstation should be considered.. ev. Also, other heuristics/metaheuristics can be developed to solve the MPUL balancing problem and their performances can be compared with that of the MPUH. In doing so, different model sequencing procedures may also be integrated into the model so that the model sequencing and. ie. the line balancing problems can be solved simultaneously.. w. As the efficiency of a production system is strongly related to its ergonomic conditions, considering ergonomic issues when designing assembly lines is gaining even more importance. On. in recent studies. For this reason, the current work can also be extended considering the physical strains, psychological strains, working postures and skill levels of the operators. Furthermore, some slackness may also be allowed for operators during their working period. This will have. ly. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60. Page 24 of 37. significant effects on the performance of the operators because zero idle times may result in more mistakes which yield reduced efficiency. Finally, standing on hard surfaces for a prolonged time can produce circulatory problems in the legs and feet of operators. Therefore, workplaces should allow enough room for operator movements.. References Bard, J. F., E. Darel, and A. Shtub. 1992. "An Analytic Framework for Sequencing Mixed Model Assembly Lines." International Journal of Production Research 30 (1):35-48.. http://mc.manuscriptcentral.com/tprs Email: ijpr@tandf.co.uk.